The
reader who has followed the investigations in this book closely up to this
point, thought over their content, and above all experienced them, will wish to
see in this closing chapter a certain summation of what has been achieved thus
far. Admittedly, only an attempt can be made at this, in which both reader and
author will do well to retain that kind of reserve that is inevitably necessary
in such attempts: the general caveat of the insufficiency of human endeavors at
understanding. The apparent apodictic quality of the following conclusions
should therefore be understood only in the sense of a formulation appearing as
correct to the author at the time.

As
an interpretation concept, we choose “cosmogony” and use as its basis the
systematic embodiment of akróasis, the “P”. “Cosmogony” means the study of the
emergence of worlds; a significant, indeed enormous, frightening term, if we
grasp it in its full breadth and depth. We will see whether and how we can
treat it fairly. The accusation of inappropriately introducing and modifying
the word and concept of cosmogony (and cosmology), used commonly in earlier
times, can be dealt with simply by a reference to the Kosmogonie of Christian
Von Ehrenfels (Jena, Diederichs, 1916), the modern founder of gestalt research.
Here the concept of cosmology was awakened once again in its original meaning, under
which we also have taken it up, whereas for example the cosmogony of Kant and
Laplace was marked by a purely astronomical and natural-scientific attitude.

Regarding
the “P” partial-tone coordinates, the reader will have been persuaded by studying
§53 that it does not represent a simple intellectual scheme, but instead that
both its entire form and its “selections” contain forms in themselves, which
are expressively, constructively, and creatively active in nature and in
our psyche. These akróatic forms thus have a reality character that is not
regulative or analogizing, but instead constitutive, and as such they are
indicators for us of realities in the highest sense. But the same goes for this
as for all “realities”: they have their own voice, their own language, and each
new language needs not only to be learned but also to be understood in its
innermost nature, regardless of the individual character of those who speak the
language. At this point there will always be a source of misunderstanding with
regard to interpretation, and therefore one would do well to accept these
“sources of error” as inevitable, not least as regards the harmonic diagram.

In
what follows, we will proceed in each case by first indicating the harmonic
phenomenon—which can be done very briefly since it has mostly already been
discussed—then draw the cosmogonic conclusion, add a commentary to it, and
finally examine what history has to say to us about our conclusions. As in all
our “ektypic” examples, the following can give only a small limited selection.

Our
analyses will use the 1/4PE in its familiar
modifications, and will use the polar depiction of the “P” in only one case,
where it is shown to be appropriate. First of all, we use as a basis the 1/4PE9 in the location and “variation” shown in Fig. 471:
here, the tone d is set as the
generator-tone. This is firstly to show how it also “works” with other tones—the
logarithms naturally remain the same, i.e. 1/1 also has
the log 0.000 here, 3/1 has log 1.585, etc.—and also
because in this case the signs and are symmetrical to d on both sides, as we already see from the circle of fifths:

...asesbfcg

d

aehfiscisgis...

└──────────────┘

└──────────────────┘

└───────────────────────┘

In addition, most of the scales
derived from 1/1d
have a C-major character (analogous
to 1/1c = B-major), so that in the choice of this
generator-tone, the “Dorian” background becomes especially conspicuous.

Commentary: We did
not arrive at this highest of all harmonic concepts of the 0/0
deductively, setting it at the beginning of the “P”, but instead inductively,
following the generator-tone line and the equal-tone lines back beyond 1/1.
This is exceptionally important for harmonic deduction, because it is precisely
through this induction that we are forcibly led to this concept; so here we
believed ourselves to be justified in speaking of a “harmonic proof of God,”
i.e. the factual existence of an ultimate spiritual reference-point.
Admittedly, our statements about this concept can only cling to words, such as
totality, everything, groundlessness, eternal rest, etc., which attempt to
express something for which there is no adequate term in any language, and for
which 0/0 is simply the most accurate symbol.
Mathematically, 0/0 can be every number, thus the
totality of all numbers; therefore it meets with our definition, which indeed
includes not only numbers but all being-values. Since the doubled zero is not
arbitrary as a quotient (0/0), but instead is forced upon
us in the mathematical-symbolic sense, we will henceforth pay special attention
to precisely this expression, and draw our conclusions from it.

History

In
§25, we already indicated those concepts of God, or better, Deity, that are to
be identified with the 0/0. They are the “impersonal”
concepts of God, concepts of a totality of all beings, all substances, the
“Brahma” of the Indians, the “Nirvana” of Buddhism, the “Tao” of the Chinese,
the “Ensoph” of the Kabbalah, the “groundlessness” of Jakob Böhme, the
“absolute being” of Hegel, and finally the “unknown God” of modern Europe.

Opinions
are divided regarding the ancient Judaic concept of God. In any case, the
precise translation of the beginning of the Bible reads: “In the beginning,
Elohim newly created heaven and earth.” The words “In the beginning” (bereshith)
would be better translated “in principle”; bara means not only “to
create,” but also “to create anew,” and—this is especially interesting—“Elohim”
is known to be a plural, thus corresponding to our harmonic symbol 0/0,
which then created, or created anew, “heaven and earth,” i.e. the polar
principles 1/∞ and ∞/1.
This “new” creation, however, assumes worldly conditions already gone by, and
is not a creation from the Nothing, but at least a creation from existing
possibilities. The metamorphosis of the “Elohim” into the later “Jehovah” or
“Yahweh” then corresponds to the step from the 0/0 to the
1/1.

In
the esoteric Indian teachings of the Upanishads, it is said, with an
astonishing degree of philosophical wisdom for those ancient times, that the
primal condition of things, the primal-being, i.e. the Brahman in the later
sense, was “na a sad, na u sad” = “not being, but yet also being”
(Deussen: Allgemeine Geschichte der
Philosophie, vol. I, 1894, part 2, p. 117). A direct description of our
harmonic symbol 0/0 can be found in a stanza of the later
Upanishad: “Two things are latently contained in the eternal, endless highest
Brahma: knowledge and ignorance. Ignorance is fleeting, knowledge is eternal,
yet he who ordains them as Lord is the Other.” (Deussen, ibid., p .120)

“Knowledge”
and “ignorance,” however, are both merely synonyms for things that are finally
inexpressible, indefinable. “The Being that is Brahman should not be understood
as the kind of being that we know through experience, and is, as we have seen,
much more a non-being in the empirical sense. The depictions of the Brahman as
the perceiving subject in us are accompanied, as a rule, by the assurance that
this perceiving subject, the ‘perceiver of perception’ will remain eternally
unknowable in itself, and merely indicate that the Brahman is devoid of any
objective being” (Deussen, ibid., p. 133). Friedrich Schlegel (Über die
Sprache und Weisheit der Inder, Heidelberg 1808, p. 247 ff.) translates the
following passage from the very ancient
Laws of Manu:

“It is said:

Once all this was darkness,
unknown, and unspecified,

Unrevealed, unknowable, as if
completely sunken in sleep,

It was the blessed self-subsistent,
discoverer of the undiscovered,

The beginning of being, that
steadily grows, that powerfully destroys the night,

That which is never to be grasped
through sense, invisible, ever-inconceivable,

Which meditating, wanting to create
many beings from its own body,

First created water, then the light
of the sun was engendered.

The sun was like a shining gold
egg.

In it lived Brahma, lord of the
universe, through his own power.

In the egg this deity then sat idly
for a year,

Then he himself divided the egg in
two by his thought,

From the blessed pieces he then
created Earth and Heaven…”

Regarding
the above lines, and many other obviously number-harmonic passages in ancient
Indian wisdom, an admonition in the Upanishads (Ramap. 84) is very noteworthy:
“Do not give the diagram to the common people!” (Deussen, ibid., pp. 13
and 68). One may well conclude that even then, the initiates taught their
students by means of symbolic geometrical figures, in a similar way to the
Pythagoreans.

The
Buddhist concept of “Nirvana” is outlined in the following manner in the Udana,
section 8, Ch.
I: “There is, O monks, this domain where there is no earth, no water, no fire,
no air, not the domain of the infinity of consciousness, not the domain of nothingness,
not the domain of neither-perception-nor-non-perception, not this world, nor
that world, nor both, nor sun and moon. That, truly, monks, I call not-coming,
not-going, not-remaining, not-vanishing, not emerging. Not fixed, not movable, without
support. It is the end of suffering [Nirvana]” (Paul Dahlke: Buddhismus als
Religion und Moral, Munich 1914, p. 171). Also, Theodor Stcherbatsky states
the following among a few orthodox statements regarding Buddha: “The true being
(Nirvana) is not knowable. It can only be defined from the negative side, insofar
as it is opposed to the entire knowable world of appearances” (Erkenntnistheorie
und Logik nach der Lehre der Späteren Buddhisten, tr. O. Strauß, Munich
1924, p. 82). Here the agreement with the harmonic symbol of the 0/0
is evident.

The
concept of the “Tao,” for which there is no adequate expression in European
languages, was not invented by Lao Tzu, who presents himself often enough as
merely a preserver of ancient traditions. In the investigation of the
relationship between the 0/0 and the 1/1,
we will delve more deeply into the origins of the highest concepts of ancient
Chinese wisdom. In the treatise Das Geheimnis
der goldenen Blüte (Munich 1929, p. 11, tr. R. Wilhelm, introduction by
C.G. Jung), which is based on earlier traditions of Taoism, the beginning
reads: “The Master Lu Tzu said: That which exists through itself is the Tao.
The Tao has neither name nor form. It is the One Being, the One primal spirit.”
In complete opposition to the non-speculative tendencies of Confucianism,
predominantly directed towards the practical, a metaphysically oriented
movement appeared within it. “A unique speculative life was awakened in this
school in the 12th century through the great sage Chu Hsi (1129-1200),
who wrote about every course of life and assigned a place in the system to
everyone, thereby solidifying the Chinese world of thought for many centuries.
He went considerably further than Confucius with the natural-philosophical
observations in his Sing-li (= natural
law), in which, schematizing and developing the metaphysical views of the Ching, he arrived at an impersonal primal being, which reveals
itself as eternal order” (Brockhaus).

The
highest Egyptian deity is Atum-Re. “I am Atum, who was alone in Nun (chaos); I
am Re with his shining, as he began to rule what he had created,” reads the
Book of the Dead (F. Roeder: Urkunden zur
Religion der alten Ägypter, Jena 1915, p. 239), corresponding perfectly to 0/0
→ 1/1 in harmonic symbolism. “I am Re, the lord of
the light-rays” (ibid. p. 266)—we need only remember our concept of the
“equal-tone lines” radiating out from the 0/0 in order to
obtain an even closer harmonic parallel.

The
Babylonian poem of the creation of the world begins with these lines:

Here, as in almost all
Babylonian legends of the creation of the world, a kind of chaos is assumed, a
primal condition (=0/0) from which the two principles of male and female emerge. Diodorus Siculus
(II, 30) writes: “The Chaldaeans claim that the world is in its nature eternal,
it has never had a beginning and can also never end; but through a divine
authority all is arranged and cultivated, and also all changes in the heavens
are neither effects of coincidence, nor inner laws (!), but instead a definite
and unchangeably valid decision of the gods”—or, as we would say harmonically:
the norms.

Kabbalistic speculation,
as it is concentrated in the Zohar,
says the following about the absolute primal origin, the “En-soph”: “Before the
ancient of the ancients, the hidden of hiddens [revealed itself], there was
neither beginning nor end ... in the Book of Secrets it is imparted: the
ancient of ancients, the hidden of hiddens, has a certain form and thus far [up
to a certain point] can be known. But it is once again unknowable, because it cannot
be sufficiently grasped [by our thoughts]. Thus it has a certain form, but does
not let itself be known [in its most innate Being], because it is the ancient
of ancients [= the absolute primal origin]” (Zohar III, 128a, Idra Rabba. From Erich Bischoff: Die Elemente der Kabbalah, vol. I, Berlin 1913, p. 93). One
should meditate upon this passage from the viewpoint of our symbol 0/0! Yet more interesting, in the sense of
akróasis and for the meaning of the auditory (voice, word) in Judaic thought,
is the following passage from the Zohar
I, 246b (from E. Bischoff, ibid., p. 90):
“Come and see! Thought is the origin of all that is. But it is unknowable from
the beginning and closed within itself. When it begins to develop, it comes to
a point where it becomes spirit. It is then called understanding and is no
longer closed within itself. The spirit develops itself again in the midst of
the secrets that still surround it, and the voice arises that is the epitome of
all heavenly choirs. This forms itself by virtue of its spiritual origin to
articulate sounds and certain words. In this, with close observation, one
notices that thought, spirit, understanding, voice, and word are a single
thing, and that thought is the origin of all that exists, and that no
interruption is present for it.” The harmonic symbol 0/0, as a reference point of all equal-tone rays,
stands as an expressive term behind the following passage from the Zohar (ibid. p. 96): “When the hidden
wished to reveal himself, he began to bring forth a shining point. Before this
illuminating point had broken through and become visible, the unending
(En-soph) was completely hidden and spread no light.” The “mathematical” 0/0 is defined quite modernly in the TikkuneiZohar with these words: “You are One but not in the number, thought
grasps absolutely nothing of you. In you there is nothing imaginable, no form
and no being” (Molitor: Philosophie der
Geschichte, II, 1834, p. 247).

Jacob Böhme (Sex Puncta Theosophica, I, 7) sets the “groundlessness” as the highest principle: “Thus, the first
will is a groundlessness, to be regarded as an eternal Nothing, and so we
perceive it just like a mirror in which one sees one’s own image, just like a
life, and yet it is not a life, but instead a figure of life and of the image
of life.” Here, also, we need only imagine ourselves as a tone-point, i.e. as a
being-value, and look to the 0/0 along the “direction” of the equal-tone line
(“mirror”), and then we have a precise harmonic correspondence. In more recent
philosophy, Böhme’s concept of “will” has been equated with that of modern
philosophy (Schopenhauer etc.), and taken as anticipated by Böhme. But Böhme’s
“eternal will” is not merely to be grasped voluntarily. Böhme writes (I, 13):
“So the mirror of the eternal eye appears in the will, and generates another
eternal basis of itself in itself: this is its center or heart, from which the
sight of eternity always arises, and through this the will becomes astir and
active, namely of that which generates the center.” Harmonically, we interpret
this passage thus: only when the “mirror of the eternal eye” 0/0 “generates another eternal basis of itself in
itself,” i.e. looks at itself, becomes conscious, which we can express with the
term 0 ↔ 0, only then does the will become “astir,” i.e. becomes our
modern active concept of will, and appears in the 1/1, i.e. in the first conceivable “vibration,”
the actual Being, the creator-word “Let it be” (= Fiat).

As a conclusion to this
historical excursion, we share yet another definition of the “nature of God”
from the Catholic Kirchliches Handlexikon
by M. Buchberger (article: “Gott”):

“God
is really and substantially different from the world and inexpressibly elevated
above all that is outside of Him and that can be thought (Vatic.). As the
self-existent and necessary Being, God stands so far above the world of created
and contingent being that He does not connect with it, even in the highest
sense. Through this, in contrast to pantheism and monism, every possibility of
mixing and combining with the substance of the world is excluded, as is every
relationship of substance to the worldly manifestation as though to modi and
accidents of the one Divinity. God cannot be ‘seen’ (1. Timothy 6:16), but only
perceived through the ‘intellect’ (Romans 1:20), he is ‘spirit’ (John 4:24), ‘one singular, completely simple and
unchanging spiritual substance’ (Vatic.), thus a personality above the world.”

How a “personality” should suddenly spring from this absolute transcendence
of the divine—that is precisely the problem that the “intellect” wishes to
investigate, and that is the path of our following steps in harmonic cosmology.

The reader interested in
the history of religion will easily find a far greater number of related
examples in ancient myths, religions, and scholarship; but merely from the few
things imparted here, he will share the author’s deep wonder and inner awe at
the remarkable convergences, all meeting together as if at a focal point in the
harmonic symbol 0/0.

Commentary: We
obtained the symbol for the deity 0/0a
posteriori, since the 0/0 concept gives us no possibility of hearing,
measuring, and building a system from things such as frequencies or string
lengths. It is different with the unity 1/1. Here we must always begin with a phenomenal
investigation, and initially a systematization. The question immediately
arises: what concrete relationship does 0/0 have to 1/1?

Here we must traverse
the two ways, the ̔οδόνκάτω
and the ̔οδόν̔άνω (upwards and downwards). “Upwards” (i.e. retrospective), as we saw, necessarily
yields 0/0
from the results of the main “intentions” of the “P”, e.g. the generator-tone
line:

0/0

↑

1/1

2/2

3/3

:

n/n

:

∞/∞

In a certain sense, the
progress from 1/1 to 0/0
is psychophysically demanded and required. The case is completely different,
however, for the “downwards,” i.e. when we think cosmologically. Here 0/0 signifies the primal beginning, the highest
peak of the system of the world, and how should we imagine 1/1 emerging from this imaginary “groundlessness”?
It is indubitable that a monstrous chasm exists between these two symbols; if
it is bridged, then everything else follows legitimately and arises of itself.

Harmonically, we have two
possibilities of bridging this metaphysical hiatus. First we observe once again
that this double zero is necessarily yielded as a quotient from the
interpolation of the “P”. We can now imagine that the symbol 0/0 becomes conscious of itself, perceives a
“will” in itself, looks at itself, and this we can notate as above, thus:

0 ↔ 0

In this instant, the
“all,” i.e. the fundamentally inexpressible, transmutes into a metaphysical
polarity of two entities, and thereby pushes the unity 0/0 → 1/1 out of itself. This is the great act of the
deity becoming conscious of itself, and simultaneously the emergence of the
first “number,” i.e. vibration or wavelength (time or space), and of the first
“tone,” i.e. psychical value. But we can also imagine that the 0/0 symbol potentiates itself, likewise grasping a
will to become conscious of itself, to reveal itself, and we notate it as:

0°

Here, one zero-value is set
as a power of the other, and thus it thrusts the 1/1 out from itself, from its endless abundance (indeed,
speaking mathematically, 0/0 can also mean “all,” every number, just like
0°). Here there is doubtless a discrepancy between the mathematical and
harmonic interpretation.

0/0, just like 0°, has no definite meaning
mathematically, i.e. it can mean everything.

One can think of 0/0 as appearing from 01–1 = 0°, or
vice versa, but both symbols can mean every number according to the
mathematical interpretation. It is different in harmonics. In the symbol 0° we
see, at the least, a self-aspectation (0 ↔ 0) or self-potentiation of the
zero, and at this moment the quotient 0/0 becomes an entity of a different type, namely
something perceiving itself unitarily: i.e. as the unity itself. Harmonically,
the passage or emanation of the 1/1 from the 0/0 signifies a transformation in the sense of
becoming conscious of the self, a direction of the will, an expression out of
the unity of the actual, the real. We will see in the following that harmonics,
in contrast to mathematics, has definitions that are not possible in pure
mathematical terms, or that no longer make sense in mathematics, especially
regarding the symbols of zero and infinity (0 ∞). In the unity 1/1 we see the highest instance of all that is
factual and real, and thus the realization of the first being-value itself.
Through the birth of this first “generator-tone,” the unity-tone is also
attached to the unity 1/1, i.e. the material (number) is placed next to the psychical (tone), or joined
with it a priori, like body and soul.
Since this first being-value (1/1 + generator-tone) stems directly from the 0/0—as every being-value does in later evolution via
equal-tone lines—and is aspected and pervaded by the being of this ultimate
spiritual court of appeal, body, soul, and spirit are unified here in every
harmonic “field,” and typified in 1/1. The following section will explain why we use
the ancient Chinese inverse symbol as a Psymbol for the unity (and
later in Table 472 for the entire “world-axis”).

Since every being-value
“is” and “tones,” and this can only occur on the basis of the temporal-spatial
reciprocity of frequency and wavelength, time and space are also born with the
unity 1/1,
and therefore the framework for the factual existence of all being-values.

History

In §25a, we introduced
various examples from history regarding both the eidetic God-concept of the 0/0 and the Origo 1/1, and a few of the highest philosophical
system-concepts, which we broadened in the previous historical review with
regard to the Eidos. There we observed that between these two different
viewpoints, the Eidos (0/0) and the Origo (1/1), one can perform a certain classification of these highest concepts, and subsequently
of the various religions and wisdom-teachings, which can also be important for
the inner characteristics of the studies in question. Here we want to take the
reverse path and allow ourselves a possible overview, admittedly also very
limited, of whether religious studies and philosophical or cosmological systems
exist that combine the two elements, Eidos and Origo. As a result, we can say
here, without being able to prove it due to the restricted space, that although
there are doctrines which in their collective character outspokenly tend toward
one pole or another (0/0 or 1/1),
both elements are found in almost all of them, albeit in more or less strong
“potency.”

This time we shall begin
with the Christian concept of the “personal” God, whose origin is in the Judaic
concept of Yahweh, and who definitely exhibits a stark Origo (1/1) character: But even with such an explicitly
concrete and unity-affirming God-concept, we find some philosophizing over the
“nature of God” on the orthodox side (as we saw from the above quote from
Bucher’s Kirchliches Lexicon) that
has hardly anything to do with a “personal creator God.” On the other hand,
besides the almost materialistically emphasized concept of Yahweh in the Old Testament,
there is the En-Soph of Judaic mysticism and tradition, about which any
adequate statement is explicitly denied. Obviously there are eidetic elements
here.

If we understand the above
concept of God in terms of his inner nature in the sense of the harmonic 1/1, and less in terms of the actual genealogy in
the relevant pantheons (since these are by no means unified, much less complete,
especially in Babylon and Egypt, and even less so in India), then we can
introduce something like the following entities: Marduk (Babylon), Yahweh
(Bible), God the Father (New Testament), Zarathustra (Persia), Osiris (Egypt),
Mithras (Iran), Zeus (Hellas), Jupiter (Rome), Buddha (India), the Monas
(Gnostics, Neopythagoreans, and Neoplatonists), the “One” (Plato), the Demiurge
(Greek philosophy), the Monad (Leibniz), and indeed all “monistic” systems.

As one can already see in
the mythological and religious entities that have the character of the Origo,
the idea of the redeemer or mediator is bound up with most of them, for example
when Christ is different from God the Father, he is still “consubstantial” with
him. In our following cosmogonic steps, we will also see a precise harmonic
correspondence.

A. von Thimus, who gives
an exhaustive analysis of some inscriptions at the Temple of Karnak in the 15th
section of his Harmonikale Symbolik,
writes the following (II, 339), based upon Lepsius and other sources about the
Egyptian god Nubti: “Also in his earth-born form, he is one with the permeating
divine spirit that vivifies the material creation; the figure of this god
symbolizes both the creative artificer of the All, and also the world of
elementary created things, fertilized by the life-breath of the divine spirit.
But he is also symbolically the bearer of the secret thoughts that lead to a
future spiritualization and transfiguration of the ensouled human creature,
summoned to union with the divine nature and to unification with its creator.”
The inner identification of this Nubti with the 1/1 and his “mission” as concentration towards
progress (or regress) to the 0/0 should not be misunderstood. Thimus shares a
wonderful passage from the unfortunately much misunderstood Iamblichus (De mysteriis sections 8.1 and 2) on the
ancient Egyptian doctrine of the first cause (ibid. II, 453-355):

“‘Before
any true being, and before the beginnings of all things, is the One God,
predominant over the first God and King, staying immovable in the oneness of
his unified Being. For neither the intellectual nor anything else is mixed into
his Being. He is set up as the primal concept of the truly good God, who is
father and creator of himself and the sole father. He is greater and first,
and source of all things, and the primary form of the first archetypes of
Intellect and Being. From this One, the self-sufficient God has created
himself, radiating in his brilliance, thus both sufficient to himself and
father of himself. For this God of Gods is the beginning, and the Monas
proceeding from the One, and the pre-substantial = primary origin of all that
is. From him proceeds Existence and likewise Being, due to which he is also
called the Father of Being; because he himself is the Being above all being,
the beginning of intellectual things, and for this reason he is also called the
beginner of the Intellectual.’”

Thus Thimus quotes
Iamblichus. The words “and the Monas proceeding from the One” show clearly that
this entire passage is about the attempt to build the demiurgic Origo concept
of God together with that of the eidetic deity (0/0), or through words and concepts (where the
sign of the “One” is obviously used for the 0/0 concept!) to somehow clarify the relationship
between Eidos and Origo.

F. Cumont (Die Mysterien des Mithra, Leipzig 1911,
p. 125) writes: “Mithra the creator is, to use the philosophical language of
that time, the Logos emanating from God, who partakes in God’s omnipotence, and
after he, as demiurge, has formed the world, he watches over it. The initial
overthrow of Ahriman, however, has not condemned him to impotence. The struggle
between good and evil continues on earth between the envoys of the Olympian
ruler and those of the prince of demons; he reveals himself in the heavenly
spheres in the opposition of the propitious and unpropitious stars, and
reflects himself in the heart of man, the microcosm.”

Here, then, as with the
Logos concept of St. John, the Logos is considered as emanating from God (0/0), i.e. as the Origo (1/1).

Proclus (in Timaeus 155) mentions a beautiful
legend: According to Pherecydes, the teacher of Pythagoras, Zeus (1/1) changed himself into Eros after he had decided to create the world from opposites, and
to bring things into friendly symmetry and to agreeable unity with themselves.
The speculations of Plato and the Neoplatonists (Plotinus, Proclus) about the
“One” are so well known that here we can be satisfied with this simple
reference. Through harmonic analysis, Plato’s Parmenides (The Ideas and the One) in particular, and his supposedly
last dialog, the Philebus, might
receive a whole new illumination, just as all of the Platonic “dieresis” of ideas and concepts can be
derived straight from the “law of harmonic quantization” as our “P” embodies it.
(For background, Stenzel’s Zahl und
Gestalt bei Plato und Aristoteles, Leipzig 1924, is best.)

Ancient Chinese speculation places the
Tai-ki (1/1)
under the Tao (0/0) as a demiurgic principle; Windischmann writes on this in his excellent Philosophie im Fortgang der Weltgeschichte
(vol. I on China, Bonn 1827, p. 142 ff.), a book which has hardly been equaled even
today, though some of his understanding of details has been superseded
(especially regarding music and the study of numbers, for which he refers to
the French Abbé Roussier, Amiot, and others):

“The
ancients knew well that over this natural principle (Tai-ki) another ruled, ...
and Shi-tsen, an ancient writer from the Chou dynasty, says expressly that Tai-ki
has a lord over it ... further it reads: The Tao goes before the beginning of
things. Tai-ki is thus, in the sense of the ancients, simply the terminus a quo of all creatural
existence. But since this terminus is
simultaneously regarded as a beginning that proceeds from eternal wisdom or, as
we would say, as the basis for the world, as its firm coherence, thus it is
also the axis around which everything moves, including the main girder that
unites the whole building, as the sensory image of the spiritual Tai-ki, which
is the same as Tai-i (the unity). It is also called axle-tree, root, and peak
of the tree, foundation, axis, column. It is taught that it is not to be
confused with the doctrines of the disciples of Fo (the Buddhists) or with the
Nothing of the Tao-sse. It is the (positive) beginning that has been before all
things, but in reality is difficult to differentiate from them; because all
things are Tai-ki according to their type. In this sense it is also called the
axis of the world, that reaches from one pole to another and around which
everything changeable moves. Human understanding is incapable of grasping this
beginning, an unapproachable power, spiritual and inexpressible. The elements
came forth from it, and from them both the heavenly and the earthly. Obviously
the Tai-ki, since it starts from Tao, also translates as supremum principium, as far as it makes itself the foundation of
the world!”

If one uses as a basis the harmonic
assumption:

0/0→
1/1→
2/23/34/45/5... (generator-tone axis)

TaoTai-ki “axis,” “girders,” etc.

then everything is immediately clear; but one also sees how hard it is for
speculation, with simple words and concepts, to bring into our waking
consciousness that which lies in us unconsciously as a psychical form.
Moreover, it appears not impossible to me that ancient Chinese number harmonics
arrived very early at a system analogous to our “P”. The material that
Windischmann gives based on French scholars such as Roussier etc. (whom I have
not yet been able to study) and which, after over a hundred years, still
remains completely untapped, especially in the Mémoires concernant les Chinois, must be newly approached from
harmonic viewpoints. The volume Chinesische
Musik, published by R. Wilhelm at the China-Institut (Frankfurt a. M. 1927)
is very beautiful with regard to the general attitude of the Chinese
philosophers, but is more than lacking with regard to fundamental
number-harmonic problems.

The reader might be
satisfied with these few examples, which offer historical ektypics about the
relationship of the Eidos to the Origo; it will be easy for him to complete the
material.

§54.4. The Creation Triad

Expression:

0/0

1/1 d

1/2d,2/1
d¢

Psymbol:
Δ

Definition: In the beginning of the creation process,
three entities form themselves, equal in value and different in nature. In and
through this ternary, the entire form of further evolution is given.

Commentary: Just as we no longer indicate the Eidos with a single 0
but instead with a doubled 0/0, we indicate the Origo not with a single 1,
but with a doubled 1/1. The duplicate form of these terms is, as we saw, not arbitrary, but is yielded
through strict induction from the structure of the “P” itself. Mathematically,
the two series are naturally identical:

mathematic:

...1/31/2

1

23...

harmonic:

...1/31/2

1/1

2/13/1...

g,,d,dd′a′

Harmonically, not at all; because here another element of symmetry of the
intervals is expressed, which is missing from the mathematical series; besides,
through the double-signature 1/1 we first obtain the possibility of clarifying
evolution from the Monas.

This twofold setting of
the One as the simplest proportion 1 : 1 or 1/1 involves the Two a priori, since two unities are placed in relation to one another.
With this, therefore, the two is born, namely in doubled form: two units as plain
2 (two), and each individual unit as 1/2 (the half) of
the whole signature 1/1—where naturally it is not the sum or the half of 1 that is understood, but
simply the possibility of arriving at the forms of the 2 and the 1/2
from the double-concept of the 1/1. This purely spiritual deduction of 2 and 1/2
from 1/1 now
allows us, however, to set it out factually, and thereupon the ternary 1/21/12/1
is obtained as the first stage of development. Now we also understand why we
use the ancient Chinese sign for Tai-ki for the unit 1/1 above as the Psymbol. It expresses
precisely the inversion (reversion) that takes place in 1/1 as the intersection point of the two
reciprocal series—1/31/21/1 and 1/12/13/1—namely the (mathematically expressed)
conversion of numerators into denominators:

... 1/31/21/12/13/1 ...

The fact that one half of
the sign is shaded is connected with the “earthly” character of the series 0 = 1/∞1/31/2
← 1/1
and the “heavenly” character of the series 1/1 → 2/13/1∞/1 = ∞, which we will discuss later. We see
on this occasion that the Tai-ki symbol emerges as a very precise designation
of one of the highest harmonic conditions, and thus as an archetypal form
anchored deeply in our psyche.

As for the triad:

appearing right at the beginning of the creation process, here we have
harmonically three different (here = d-)
values, which are inwardly equal and yet different in nature (in their location
and pitch). Since we can not only judge the three octave-tones d,d d¢ intellectually and physically (number-measure)
but also evaluate them psychically, and since they are at the pinnacle of the “P”,
this is probably the single instance, in the history of ideas, of a
psychophysical explanation for the “mystery” of the Trinity. Compare to this our
statements in §30 of this text.

History

There is so much
literature on the trinity problem in mythology, the history of religion, and
the history of philosophy (three-step dialectics), that we cannot discuss it
further here, and must refer the reader to the few bits of information about it
given in §30a and §50.5. Anyone who seeks to obtain any degree of historic
insight can only conclude that ever since humans have thought, they must have held
the form of this ternary as one of the most important psychic prototypes in the
subconscious, a form of entirely characteristic quality which strives again and
again in the most varied domains, above all those of religion and mythology,
toward some symbolic realization. And the phenomenon of the dialectic, with its
logical triad of thesis, antithesis, and synthesis, shows that the ternary
rules the form of our thought itself. Harmonics, however, simultaneously shows
that the ternary (as a cadence : crystal surfaces!) also inhabits nature as a
form-potency; through this it is raised above its merely “anthropomorphic”
meaning and obtains a universal character—which once again explains and makes
comprehensible such a far-reaching significance in the most varied human
spiritual domains.

§54.5. The Creation-Polarity

Expression:

Psymbol:

Definition: The creation triad requires creation-polarity. Infinity
(∞) and Nothing (0) emerge, as well as the median line (1/12/23/3
...) = Origo-axis.

Commentary: In the progression from the Eidos 0/0 to the Origo 1/1 we see, harmonically, the actual process of
the world’s becoming. We can easily go on to describe the further evolution
from the 1/1, indeed we must follow a “before” and “after” here, or some kind of
progression. But this is only required by our method of expression; because
fundamentally, with the birth of the Origo 1/1 the immediate emergence of the entire cosmos
is given in its ideal form. Its temporal developments are only evolutions of
the system of the “P”. We could thus just as well have put the polarity before
the triad and discussed the subsequent creation steps in any order, since they
spontaneously emerged, as great cosmological prototypes, with the creation of
the Origo, comparable with the sudden crystallization of a substance, the
completion of a chemical process, the “brainwave” of a thought, an idea—these
examples taken admittedly only as completely insufficient comparisons. The
reader should turn his attention more to the types in themselves than to the
series-progression.

The creation-polarity, and
the Origo-axis (generator-tone line) which it necessitates, bring into the
world the concept of the Infinite (∞),the concept of the Nothing (0), and
the concept of constancy, perseverance (1/12/2 up to ∞/∞).

All three of these
concepts have vectorial, direction-giving, “intentional” character. Whereas the
vectors 0 and ∞ go out from, or back to, the origin 1/1, the vector ∞/∞ (origo-line) takes its origin from the highest
harmonic value 0/0. Cosmologically, these expressions and definitions are of great
significance.

From this, we see firstly that
the Infinite requires the concept, indeed the actuality, of the Nothing, and
vice versa. Both concepts, and not only the one “or” the other, are
intentionally posited for the reality of the creation. These two are primal
principles of the limitless (̔άπειρον) and of the limiting (περαίνοντα) of the Pythagorean-Platonic philosophy, and
furthermore the prototypes of all dualistic systems, be it in mythology,
religion, or science. But we see further that these two principles have no
direct participation in the deity 0/0 as vectors or intentions, but are instead
“origo-nally” required, i.e. are a direct emission of the Monas 1/1, the concrete act of creation. Thus in
harmonics, the two directions that embrace the Monas 1/1, the Nothing (0 = physically the “empty”
universe, philosophically the absolute privation, ethically the complete want)
and the Infinite ∞ = of the unending universe, the concept of
endlessness, (the infinite plenitude), stand in opposition to the symbol of
eternal rest, the deity (0/0), or simply eternity. We will soon speak in
more detail of the inner psychophysical content of these vectors.

These two principles are
now brought into a sensible relationship through the Origo-axis (1/12/23/3
...), which we can also call the unity-line of the world; indeed without this
they are entirely unthinkable. This unity-line, however, goes as a vector back
to the 0/0
and thus symbolizes its direct origination from the deity. Precisely this fact
allows deep speculations (Plato, Plotinus, etc.) to conceptualize about the
“unity,” while the epistemological deliberations and analyses of the concept of
the “Nothing” and the “Infinite”—if I may express myself in the mode of the
ancients—never participate in “the gods” and remain as they have remained, more
or less domiciled in purely logical spheres.

History

An ektypic evaluation of
the two vectors 0 ← 1/1 → ∞ was already attempted in §19a
ad 1 and §50.5, especially with regard to the Pythagorean concepts of the unlimited
(∞) and the limiting (0). We will add a few more examples here. If one
sees in the Origo-axis 1/12/23/3 ... the single,
cohesive element of the 0 ← 1/1 and 1/1 → ∞ vector, then one can
understand the dark declaration of Heraclitus’s riddle: “The way up and down is
one and the same” (Diels: Fragmente der
Vorsokratiker, Heraclitus fragment, 60).

“When
Pherecydes was the first to teach that souls were “eternal,” i.e. not merely
immortal, as Homer said they were, but instead beginningless and endless, and
that birth and death mean only a changing of place in the universe, this agrees
very well with the striving for reunification with the two eternal and
beginningless principles ̕Aιθήρ
(ether) and Γη̃
(earth). But of course, it can just as well be said that body and soul, spirit
and matter are imperishable and without origin. There can be no doubt that this
dualistic anthropology under Pherecydes had an ethical goal, if one remembers
that the primal origin of one element of man, Zeus-Ether, is called the
‘perfect good,’ whereas Chthonie Ge appears throughout as mother of the riotous
... foes of the gods ..., the source of everything evil and of that in man
which opposes the will of gods.”

Harmonically, we
understand souls as “eternal” when we assume the reference-direction of all
being-values as being toward 0/0. If it is true that Pherecydes explained souls
as “eternal” and “not immortal,” then this expresses that wonderful impression
that the Pythagorean-harmonic symbol of the Eidos (0/0) allegorizes so beautifully—and realizes. The
idea of immortality, to which something more or less material always clings, is
stripped of all materiality through transformation into the “eternal,” and
transposed to the highest reality of the Eidos (0/0).

The equating of the 1/1 → ∞ pole with “good” and the other
0 ← 1/1 with “evil” once again reveals the replacement of outline and possibility
with fact and reality, typical of the ancients; compare this to the following step.

The Orphic expressions ΑΙΩΝ
ΑΠΕΙΡΟΣ (unending duration = 1/1 → ∞) and NYΞ ΑΠΕΙΡΟΣ (unending night
= 0 ← 1/1) are very remarkable; they doubtless correspond to the inner psychical
configuration of our two harmonic series-pairs. If one applies the ancient
procedure of “psephoi” (gematria), as mentioned with similar examples in §17b,
substituting the corresponding number of the alphabet for every letter, then
for both double names one obtains the sum 128 = 27, the seventh
octave-power!

The two polarities Yin and
Yang (– – and —) which proceed from the Tai-ki of ancient Chinese wisdom, on
which not only the I-Ching but all of
Chinese philosophy is based, are the exact counterparts of our harmonic series-pairs
0 ← 1/1 → ∞, and their definitions as darkness and light, no and yes,
female and male, etc., show just how purely Chinese thought grasped and
manipulated a prototypical psychic form—remember what was said in §50.8 regarding
the I-Ching diagram.

A related symbol comes to
mind here, upon which Egyptological research has continually foundered, despite
its known content, namely the so-called “Ankh,” .
This hieroglyph, signifying the symbol of divine life, is known to appear even
in the earliest monuments and inscriptions, and not only in Egypt, but also on
Etruscan, Sicilian, Persian, Babylonian, and Chaldaean images, gems, coins,
etc. (Thimus II, 111 ff. with ill.). One should read Thimus on the contrast of
this hieroglyph with the sign of the cross and his deep speculations about it.
Unfortunately, Thimus, whom I so much admire, either completely missed the
simplest derivation of this Ankh, or else did not think about it at all, since
it seemed self-evident to him. Namely, if one draws the “P” with basal series
not bent at a right angle but lying along a line, with the 0/0 point as a circle above and the generator-tone
axis directly below, then the result is Fig. 471a.

Figure 471a

One must admit that for
the most important laws of the “P”—Eidos, Origo with its three “directions”—no
better graphic image-concept could be found. This same symbol, so widely used
in Egyptian hieroglyphics and on Egyptian reliefs, allows one to assume with the
highest probability that the system of the “P” established on the basis of the
monochord was known in the secret schools of Egypt,
and that Pythagoras brought the system from there to Greece.

The ancient Babylonian
doctrine, still echoing in the cosmogony of Berossus, of the emergence of the
world of the senses from the unification of a creating male and receiving
female, birthing, primal force (corresponding to the Chinese Yin-Yang principle)
is recorded in the Origenian
Philosophumenis. This “Origenes of the Heathens and Neoplatonists”—not to
be confused with the church father of the same name!—next to Plotinus the most
significant scholar of Ammonius Saccas, declares (according to Friedrich
Münter: Religion der Babylonier,
Copenhagen 1827, p. 46): “Diodorus the Eritrean and the musician Aristoxenus
say that Charatas the Chaldaean taught Pythagoras this: two are the principles
of all things from the beginning; a paternal and a maternal. One is light, the
other dark. Qualities of the light are warmth, dryness, lightness, swiftness;
to the darkness belong the cold, damp, heavy, and sluggish. And from all these,
along with man and woman, emerges the world, and there is a musical harmony.”

The Neopythagorean
Numenius of Apamea (2nd century a.d.),
forerunner and influencer of Plotinus, “founder of the doctrine of the three
deities following one another in rank: the highest principle νου̃ς, the demiurge, and the world” (Überweg, Geschichte der Philosophie, vol. I, 1926, p. 514), assumes a
principle (0/0) that is timeless, eternal, always the same as itself, spatially
unmovable, unchanging, simply being. But since the world cannot be identical
with this absolute, a second principle must mediate: the demiurge (1/1).

“Numenius
differentiates first the world-maker (δημιουργός)
from the highest god as a second god. The first god is good in and through
himself; he is pure thought-activity (νου̃ς) and principle of being (ο̕υσίας̕αρχή)
and as King (βασιλεύς),
free from all labor. The second god (demiurge) is good through participation in
the nature of the first; he looks at the supernatural primal images, works with
matter, and thus sculpts the world, in that he is the principle of becoming.
The world, the product of the demiurge, is the third god. The basis for this
doctrine was first supplied by the demiurge and the divine world of the Platonic
Timaeus. But the overseer (demiurge),
to whom the same original ideas apply, cannot be the highest court of appeal in
the longing for absolute divine transcendence. Thus a higher god prevailed over
him, to whose designation the Platonic ideal of the good and the Aristotelian
placement of the deity as the basis of the pure νου̃ς offered a footing, perhaps with a contribution
from the character of the βασιλικη
επιστήμη (royal knowledge) from Plato’s
Politicus, 305d. Also Plato’s Sixth
Letter comes into consideration.”

(Überweg, ibid. p. 521). Now, when Numenius, as Proclus tells us (in Timaeus III), “traced the soul back
to numeric relationships,” and, according to Eusebius XI, 22, commends
penetration of the numeric secrets as the way to knowledge—just as for the
Pythagoreans, the source of all Platonism (Eusebius IX, 7 and XIV, 5)—then the
presumption is allowed that Numenius probably used direct Pythagorean
traditions as a basis, and knew of the Pythagorean “P” system in some form.
When he designates his three deities (besides the titles Nous and Demiurge)
expressly with πατήρ (father), ποιητής(overseer,
demiurge) and ποίημα (the created, the world), the harmonic succession 0/0 → 1/1 → “P” is so obviousthat no doubt can remain that he was a true and not merely “syncretistic”
Pythagorean.

Finally, I will give a few
more interesting related Kabbalistic passages from the strange work already
mentioned above. Anonymously published in his own time, Molitor’s Philosophie der Geschichte, oder über die Tradition
(Münster, 4 vols., 1834 ff.) treats “the tradition in the old covenant and
its relation to the church of the new covenant, with especial reference to the
Kabbalah” in a most thorough and profound manner, and should have been
republished long ago as one of the most important spiritual products of the
Schelling-Baader era. In the appendix to vol. II of his work, Molitor offers a
few passages from Kabbalistic writings (Zohar
etc.) in Hebrew and German, from which I choose the following:

Of the Ain-soph, it is
said: “Before the world was created, He, the [Most Blessed] and His name were one.”
“He created the tangible from the void and made its nothing into something.”
“Even in the minerals, like dust and stone, there is necessarily life and
spirit, and a star or watchman over it.” “Ain-soph is separate and removed from
all imaginable. It comes before all emanations and creations, and in it is no
time.” The Kabbalists distinguish the Being from the Light within the Ain-soph,
and say that the world was created from the light. Etz ha Chaiim tells us, in
the passage: From Ain-soph came out a straight, fine line in the manner of a
canal: “Only the illumination of Ain-soph, but not its Being. This is what the
doctrines say: it is the place of the world; but the world is not its place. For
its Being does not extend itself, but its light does.” Here think of the
equal-tone rays from the harmonic symbol 0/0!

§54.6. The Creation of Paradise and the Spiritual World

Expression: (Fig. 472)

Psymbol:
×

Definition: The first senary evolution cycle of the “P”
creates a world of pure major and minor chords, mutually pervading each other,
a pure “paradisiacal” world that ends in the seventh ratio-series as a closed
index, repeating itself again in several “senary” series-groups and
series-pairs, but these become ever rarer in the course of further
differentiation. Thus we can with good reason conceive of the closed complex PE6
(as well as PE8) as a world of pure chords reposing in
themselves, as a domain of pure harmonic conditions, which is unique in its
type and represents the first cycle of harmonic cosmogonic evolution.

If one now builds a pure
spiritual world behind the 0/0, on the model of the imaginary basal series 0/∞
← 0/10/01/0 → ∞/0,
which can happen purely constructively and is shown in the upper sector of Fig.
472, then we see in this imaginary “P” domain to a certain extent the spiritual
prototype for the “real” “P” realized in the lower sector. The reader is asked to
inwardly grasp the illustration of Fig. 472, i.e. the “above,” “below,” as well
as the variation and combination of the “P” given there, in terms to its form; of
course, we can also lay it on its side, place one of the two imaginary basal
series upon the other, choose the hexagonal form of the illustration, etc. This
imaginary, purely spiritual world has a much simpler structure compared to the
real “P”. Its axis is the 0/0-axis, that of the Eidos. At the left we see
only vertical 0-series of identical spiritual values; to the right we see only
vertical series of the spiritual “whole numbers”; we can no longer logically or
material-mathematically grasp the terms of 0/3 and 3/0,
for example, as quantities, but instead as purely spiritual values. A spiritual
zero-world appears in this upper sector left of the 0/0 line: to the right, the metaphysical “birth”
of the whole numbers. We have not reached this arbitrarily, but through
retrograde interpolation of the “P” in a strictly legitimate way, similarly to
how we arrived at the elicitation of 0/0.

Commentary: The reader has been carefully instructed in previous
chapters regarding the “senarius” and its closed core in index 6 of the “P”, as
well as regarding the “ekmelic” character of the seventh-series, being the
first beyond the senary. In Fig. 472, we attempt to show the corresponding
difference between the “spiritual,” “emmelic” (senary), and “ekmelic” (outer
senary) central ratio-builders of the vertical middle axis by leaving the
ancient Chinese Yin-Yang symbol “empty” in the first case, half-shaded in the
second case, and filled out in black in the third case. Through this, we obtain
a clear optical image of the conditions in question.

Figure 472

It is now the time to
discuss summarily the problem of the transcendent signs, becoming especially
important in Fig. 472, 0, ∞, 0/∞, ∞/0,
∞/∞, etc. For the mathematician, 0 and ∞ are still unequivocally
ratio-based concepts: “zero” and “infinity.” The definition of 0/0, which can mean “all,” i.e. every number, is
more difficult for him, and the terms 0/∞, ∞/0,
∞/∞, ∞, ∞/n, have hardly any meaning for
him.

Let us look at what
harmonics says to this (see Fig. 472). Let us begin with the perpendicular
middle axis. In the upper domain, up to the middle field, which belongs to both
sectors, it has the value 0/0. The mathematical conclusion “everything”
agrees with the harmonic one here, even if this naturally also attains the
greater amplitude, since the harmonic concept of 0/0 designates the highest concept of the Eidos
reachable in us. In the lower domain we find the value 1/1, generally speaking n/n, which is mathematically equal to 1. Harmonically,
however, it is evident that besides the unity (Monas), the situs, the place, i.e. the location in the field, also plays a
role. Thus the 1/1 is different from 2/2, 3/3, etc.
in its position, since it must obviously be ascribed an exceptional rank in
contrast with the other units. The units 2/2 ... 6/6
are once again different from units such as 7/7, 11/11, 13/13 etc., since these units represent
intersection points of ekmelic series-pairs. Here, therefore, we have three
different characters of units, whose being-values are the same but whose
field-value within the “cosmological” succession is different. This difference
applies only in the topological sense, not in the ontological, and can be taken
into consideration only in judgments of location, not in terms of being. It is
interesting that the vector of all these units 1/12/23/3
... ∞/∞ leads to a doubled infinity ratio, which we must view harmonically as the
maximal Being, and cosmologically as the end of the development of the world.
If this point is reached, then ∞/∞ ignites itself upon 0/0 and the entire world-system is cleansed again
in an enormous melting process. As for the imaginary basal series that belong
to both sectors:

0 = 0/∞ ... 0/20/1 ←

0/0

→ 1/02/0
... ∞/0 = ∞

with regard to the symbol ∞ = infinite, we are still in agreement
with mathematics, though harmonically we grasp the concept of infinity not only
in terms of size, but as the infinity of the being-values. The term 0 = zero,
on the other hand, can mean the mathematical Nothing or a limiting value (limes), while harmonically, we grasp it
more in the sense of an absolute lack (ethically), a thickest concentration
(materially), and simply a limit (in the sense of not being able to go any
farther). It is these two imaginary series, coupled in the 0/0 value, that represent the communication
between the “lower” real world and the “upper” spiritual world. Parallel to
them, in the lower (material) sector, run only series of the limited form 1/∞2/∞3/∞
... or ∞/1∞/2∞/3 ... which,
taken themselves again as vectors, tend in both cases toward the maximal
being-value ∞/∞. The corresponding parallel lines in the upper (spiritual) sector, on the
other hand, always collectively observed from the 0/0 line, have the limited form 0/∞0/∞0/∞ ... or ∞/0∞/0∞/0 ..., and do not
construct any recognizable vector tendency, whereas the not yet limited
parallel lines, for example 0/50/40/30/20/10/0 or 5/04/03/02/01/00/0, all turn themselves from the imaginary basal
series toward the highest 0/0 value. Whereas all concrete partial-tone
series of the lower sector still express, in their limiting values, what I
might call a “concrete” infinity (1/∞2/∞3/∞
... or ∞/1∞/2∞/3 ...), all
the analogous series of the spiritual sector, turning away from the 0/0 axis, point to the two completely transcendent
concepts, 0/∞ and ∞/0,
and, turning toward the middle axis, to the highest transcendent concept of 0/0.

The collective impression
of the spiritual sector is one of absolute repose, symbolized by the three
great harmonic-metaphysical principles of the 0, the ∞, and the 0/0, and characterized by the majesty of the
spiritual being-values1° 2° 3° ... and the connected transcendent emergence of
the whole numbers, adjoined to which we must imagine toning spiritual media,
for whose description every term fails us.

The collective impression
of the lower “material” sector is one of a temporal-spatial and psychophysical
agitation, a world of reality, into which the reflected splendor of the repose
of the spiritual sector radiates (which is especially symbolized by the middle
axis 0/01/12/2 ... and the pencil
of rays of the equal-tone lines radiating out from the 0/0), but which soon proceeds according to its own
laws, and above all in periods of certain cycles, at the beginning of which is the
“paradisiacal” cycle.

Concrete final conditions of the individual being-directions. System of
natural conditions.

∞/nRelative infinity

Concrete infinitude concepts of the individual being-directions. System of
natural laws.

∞/∞Being

Maximal Origo-value. Final state of the world.

History

The reader should not
stumble over the term “paradise.” I have used it for the first cycle of the
pure harmonies appearing in the harmonic system, to refer simultaneously to the
doctrine, appearing in all religions and mythologies since ancient times, of an
original perfect, “paradisiacal” condition of nature and the human race, a
condition of harmonic polarities, a “golden age,” in short an ideal
wish-fulfillment, which, regardless of whether we consider it to have ever been
reality or to be pure illusion, still belongs de facto among the most ancient ideas of humanity. And this is
precisely our concern here: to make conceivable and evident how one should
imagine this condition, which is certainly strange in itself. If we assume the
construction of the harmonic forms, as it is symbolized by the “P”, as a
psychophysical reality, i.e. as a prototypical form inherent to both our psyche
and to nature, then we have the explanation and interpretation in the first
senary-closed sector of the “P”, which consists merely of interpenetrating pure
major and minor chords.

The terms “paradise” and
“golden age” may suffice for the reader in lieu of further historical evidence,
which anyone who is interested can easily obtain from the literature. In philosophical
terms, as far as I know, Jakob Böhme and Franz Baader were the last and only
ones who supposed a condition of “eternal nature” on purely speculative and
epistemological grounds, a configuration of being-values originally emanating
purely from the act of creation, in which as yet no Luciferian disruption had a
part. These studies of Böhme and Baader are interesting and important, and it
is impossible to discuss them with any thoroughness within the framework of
this text.

The idea of the correspondence
of “below” and “above” is also ancient, and has taken form in countless
mythological emblems and religious, as well as philosophical dogmas. “The whole
lower world is made according to the model of the upper world. All that exists
in the upper world only appears to us here below as in an image, and yet both
are the same” (Zohar II, 20a, from E.
Bischoff, ibid., II, p. 99). From the point of view of Fig. 472 and its upper
and lower sectors, perhaps the following mysterious passage from the Zohar (III, 292a, b, ibid., p. 102)
becomes understandable: “There have been old worlds that were destroyed again
immediately after their emergence, worlds without form, which are called
sparks, just like sparks that the smith lets fly in every direction when
forging the iron, and which die out immediately. These sparks are the original
kings of the ancient worlds. They were destroyed and could not exist, because
the Old One, blessed be his name [0/0], had not yet taken his form [1/1], a form that represented itself in the male
and female, because the two light-faces, revealing themselves in nobility and
justice, did not yet look each other in the face [i.e. because the condition of
the becoming conscious of the Eidos 0 ↔ 0 had not yet entered!] and the
overseer [1/1] was not yet at his work.” Consider, furthermore, the concept of the
“angel” and “blessed spirit,” Plato’s Allegory of the Cave, and all the
alchemical ideas (going back to ancient Hermetic writings) of the correspondence
of an upper spiritual and lower material sphere, ideas that again have their
origin in the notion, common to all the idealistic philosophies since ancient
times, of a pure world of thought, toward which the Being of nature and humans
directs itself. In the upper sector of Fig. 472, we have obtained an
image-concept of this “angelic” world, namely in the same way as in all our
harmonic diagrams: not arbitrarily, but through strictly legitimate
interpolation of the “P” itself.

The world of the gods has
always been inherent to human thought and perception: it is an image of higher
beings, gods, saints, concretizing in the human type of the genius and
sublimating philosophically in a world of values. We can identify this
harmonically with the first great senary interval-forms (octave, fifth, fourth,
thirds, and whole-tones), which appear again and again and “reincarnate” in the
different P-cycles as meaningful value-concentrations. We can extract
these great forms from the “P” system as “interval-power diagrams” (see the
fifth-diagram, the fifth-third diagram, etc.) and will find exceptionally
important conclusions about certain problems from the isolation or “rendering
independent” of these primary interval forms. In the following section, the
fifth-diagram will give us such information.

In the above, we have
attempted to describe the first harmonic evolution cycle, which we have closed
with index 6, and constructed the “spiritual mirror,” an imaginary world which
is only approximately signifiable with familiar mathematical symbols, but which
we are forced to accept from the “retrograde” interpolation of the “P”. Now we
will leave this imaginary world, whose further progress is indeed unequivocal,
to itself, and in the last section observe our harmonic cosmogony of the entire
“P” system of index ∞.

§54.7. The Creation System and
the Earthly World

Expression: The entire “P” system.

Psymbol:

Definition: Every cosmogonic development has a beginning
and thus also an end, even when we set the “limit” to ∞ = infinite. Since we can well imagine such harmonic
diagrams, but can only produce them graphically up to certain indexes, the
reader must use his powers of imagination to help here, and check the following
statements on previous diagrams.

Commentary: Now we shall try to describe the further “progression”
of harmonic cosmogony—which we can only ever illustrate successively, although
in principle it is realized simultaneously with the 1/1—in its further important great forms; and to attempt
an interpretation of these forms.

With the Six as the ratio-builder,
the core of the mutually consonant pure chords is closed, and with the Seven, a
foreign element intrudes for the first time. These heterogeneous steps then
repeat themselves in ever-increasing sequences:

so that the entire “P” system is obviously underlain by an ever-increasing
differentiation, whereby the possibility of consonance becomes ever more rare and
difficult. On the other side, however, the senary steps “reincarnate” again and
again, only they “become isolated” at increasing indexes, and finally almost
disappear in the mass of non-senary material; but they have such great
significance precisely because of their value-weight. One can imagine that the
differentiation leads to confusion at a certain point, and regeneration can occur
only through a self-metamorphosis of being-values or through a return to an
earlier, simpler index, in which the ratios are still simple and comprehensible.
The self-recollection, the “monastic” or “ascetic” way, is symbolized by a kind
of “potentiation” that we can notate harmonically on some ratio, such as 22/34
or in general x/y, thus:

22°/34° or x°/y° = 1

i.e. self-potentiation by means of the doubled zero-symbol 0/0 leads every being-value back to the 1/1 and thus back to the Origo. The individuality
is extinguished here, and changes itself back again in the act of creation. The
second way of “regeneration,” i.e. the withdrawal to simpler conditions, is
only imaginable collectively. History provides countless examples for the two
possibilities. It is easy to see one
of the origins of worldly evil in this ever-widening differentiation and
complication, which must finally lead to lack of orientation. And from here it
appears—we have already discussed this—that only on the basis of certain
normative selections within the “P” system can a means of healing against this
excessive splintering be created and found, which has happened de facto for a long time in the arts,
through ethical principles, social regulations, etc., and which symbolizes our
above mentioned “regeneration” only singularly or collectively. Another
“concrete” condition of the worldly evil can be seen in the sudden appearance
of the first “ekmelic” seventh periods and the things that follow it. In the
sense of harmonic consonance, i.e. of the possibility of a real and not only
“statistical” world harmony, these ekmelic ratios are actually elements of
disturbance, while in contrast the great harmonic senary steps try again and
again to substitute themselves, not only “psychologically” but cosmically, as
Kepler’s investigations and our own contributions prove. This entire Textbook
attests to this in our ektypic excursions. The most visible harmonic evidence
for a domain of “light” and “darkness” appears, however, to be the dualism
already immanent in the very peak of the Origo, which takes effect in a
thoroughly polar manner in the > 1 and < 1 sectors of the
“P”-development, and which we find expressed symbolically in the most varied ancient
mythologies and wisdom-teachings. But precisely this interpretation, i.e. the
anchoring of worldly evil in dualism and the reflection of good-evil in an
original polarity, already appears untenable to me, because we find this dualism
in the purely senary domain of the PE6 and cannot possibly
include the “thorn of evil” in the pure major and minor chords appearing here. In
this supreme dualism, i.e. in the Origo itself, a deeper, meditative
contemplation can certainly see the possibility and the anchoring upon which the
world-catastrophe must occur, with the index raised to the maximum, i.e. at the
highest tension between vast concentration 1/∞ = 0 and vast expansion ∞/1 = ∞, together making ∞/∞; and from this tension inherent to every index
of the system an original transcendence
of evil in “eternal nature” may be derived—as was done by Jakob Böhme and, in
more primitive form, by the ancient dualistic systems and religions. But
important and interesting as these designations of the “possibility” are, our
interpretative consciousness seeks more “real” reasons, at least an explanation
for how dualism hardened and isolated itself in contrast with the highest
instance 0/0 and its deputy 1/1.

Here, in our harmonic
selective diagram, we have sharply indicative evidence that is just as
remarkable as the problem itself, namely in the so-called “fifth-diagram,” i.e.
the interval-power diagram of the fifth, which we technically discussed in
§39.2e and §39.3b. This fifth-diagram, built on only one ratio—namely the three
with its powers and reciprocals, thus the first and most important interval after
the octave—has a thoroughly hierarchical structure in contrast with the
overtone diagram (from which it indeed represents a selection), and because of
its interval (the “dominant”), it embodies, in a certain sense, a “divine
world”: a world that does not yet partake of the major-minor dualism and is
genderless, appearing to express purely linear principles (identical
tone-lines, whole-tone scales, material for diatonic, chromatic, and finally
enharmonic scales) in unapproachable perfection.

We already noticed, in
§39.3b, that there is a strange tendency in this diagram to “manage without”
the generator-tone. Indeed, not only that. The inclusion of the generator-tone
line somehow “disturbs” the construction of the scales, which can be derived
without it and without “hiatus” in the right and left sectors (see Fig. 473) by
means of the “substitute generator-tones” his
and deses.

Figure 473

This “adversarial”
relationship between the two sectors becomes completely clear if we draw all ratios of this fifth-diagram
including the generator-tone in a polar projection (Fig. 474).

Figure 474

For comparison, the 12
tempered semitones are drawn in dotted lines (30° 60° 90° etc.). Here we see
plainly how the two “adversarial” camps have their own succession in their (1/n)n
and (n/1)n powers, and neither needs the
generator-tone at all. If we write out the 1/n and n/1
series separately:

(1/3)5

(1/3)10

(1/3)3

(1/3)8

(1/3)1

(1/3)6

(1/3)11

(1/3)4

(1/3)9

(1/3)2

(1/3)7

(1/3)12

des

eses

es

fes

f

ges

ases

as

bes

b

ces

deses

Log:

075

150

245

320

415

490

565

660

735

830

905

980

Diff:

95759575957575957595757595

(5 × 95); (7 × 75)

(3/1)7

(3/1)2

(3/1)9

(3/1)4

(3/1)11

(3/1)6

(3/1)1

(3/1)8

(3/1)3

(3/1)10

(3/1)5

(3/1)12

cis

d

dis

e

eis

fis

g

gis

a

ais

h

his

Log:

095

170

265

340

435

510

585

680

755

850

925

020

Diff:

75759575957575957595759575

(5 × 95); (7 × 75)

Figure 475

then here we have two very regular chromatic scales with 5 × 95 and 7 × 75
logarithmic semitones, which appear to have nothing to do with one another. In
every case they obviously defer to the generator-tone, the “demiurge” =
creator-god, the value to which they owe their existence, and it is precisely
here that we must direct our utmost attention. For it means simply that within
the entire “P” system, the most important interval configuration (after the
octave) of the fifth expresses tendencies that press on the one hand towards a
self-isolation and emancipation from the 1/1 (Origo), and on the other hand sharpen this
isolation further with an adversarial dualism.

Here, therefore, we have
an exact psychophysical proof of an ancient mythological and religious theorem:
a fraction or dispute already entered into the “divine world,” as well as an
associated turning away from God (Origo = 1/1).

The only “synthetic”
element of the fifth-diagram, with the exception of the “evacuated”
generator-tone line and the rigid egocentric equal-tone parallels, is the
“whole-tone scale.” But precisely this, which appears to our perception as
something completely “unnatural,” demonstrates the inner psychical tension of
the diagram.

If we now return to the complete
diagram of the familiar “P”, we find, as one of the further cosmological
archetypes, the generator-tone line 1/12/23/3∞/∞ ..., running through the middle of the entire system, which we can also
call the Origo-line or Origo-axis. It symbolizes the ever-present creative
primal force that gives stability to the system and, as the deputy of the Eidos
0/0, the
actual “mediating principle” of harmonic cosmogony. Because every being-value x/y,
born of the two “intentions” 1/1 → n/1 → ∞/1 = ∞ and 0 = 1/∞ ← 1/n ← 1/1, as the intersection point of an undertone and
overtone series, must pass the Origo line in one of its “ancestral series,”
this mediating principle is inherent a priori in every being-value.
Besides, as we saw above, every being-value is able to identify itself with
this mediating principle through self-potentiation with the Eidos (x°/y°)°
– 1, to return to it, through which the naturally necessary presence of the
Origo changes itself into a self-willed “unio
katholica” (καθολικός= affecting the whole; here the Monas 1/1,
which rules and expresses the entire “P”). In terms of religious cosmology,
harmonics sees the Origo axis as the symbol for the idea of a redeemer pervading
all the thought and feeling (belief) of humanity, and in the relation of every
being-value to the Origo, the symbol for the belief in a “personal” God.

As
a final great cosmogonic form, we see the pencil of rays of the equal-tone
lines, reaching out from the Eidos 0/0, illuminating the
whole system, and imbuing every being-value. Since here every being-value has
its own unique ray, by means of which it is in direct relation to the deity (0/0)
without any other mediation—i.e. it receives its spiritual existence from the
deity—harmonics sees therein an emblem of the direct relationship to the deity,
a symbol for the “unio mystica,” a
religious attitude that was the goal of the mystics of all times and peoples.

If
we want an idea of how to imagine the emergence of the three kingdoms of nature
from the “P” system, we can say the following (cf. ill. Harmonia Plantarum, p. 288):

Figure 475a

In the crystal, the
prototype of “matter” in its macroscopic appearance, the “P” realize themselves
precisely according to the group-theoretical arrangements out of and around the
generator-tone center 1/1. Here the index plays no role as yet, as opposed to the generator, i.e.
the inner choice principle of favored ratios and certain arrangements. In
plants, the “P” system splits into n/1 and 1/n
sectors; the resulting polarity between light and darkness roots the plant in
the earth and leads to the emergence of life as a primal inner polar tension.
The index is added here to the generative selection as form-limitation, due to
which the plant, after completion of its individual life-indexes, “dies.” In
animals, the polarity receives an augmentation through the conjunction
(combination) of two independent “P” systems, which are coupled in 1/1. As the geotropic 1/n-n/1
relationship of plants disappears, the possibility of movement enters in.
Furthermore, the appearance of circular scale-structures rounds off the animal
body, forming both outer and inner “organs” and, psychically, the ability to
“hear” and to “speak”—this is admittedly meant only as an initial rudimentary expression
of a conscious manifestation of will (scale phenomenon). The next higher kingdom
of nature always absorbs the last norm-step reached by the previous one. Thus
one can say that the law of the crystallographic surface differentiation, which
is common to all classes of crystals, harmonically connects directly with the
laws of ramification, and that the norms attained in the plant blossoms are
taken up directly by the lowest representatives of the animal kingdom—clearly
shown by sea lilies, jellyfish, sea anemones, starfish, etc., whose
form-harmonics are in such striking concordance with the blossom-harmonics of
plants. In humans, the harmonic dichotomy then potentiates itself to the
highest harmony, and we become conscious
of the sense of our form as a synthesis
of the forms of the three kingdoms of nature. We are able, by means of akróasis,
to spiritually objectify the sense of this, our own form-synthesis, by means of
the “P” system, thus creating a valuable means of understanding our own Being
and the Being of the world.

Our harmonic cosmogony has
been supported until now upon the scheme of the quadratic 1/4PE, which indeed forms the
foundation and starting point of all harmonic systems. If we now convert this
system into polar coordinates, then we obtain an image that simultaneously
illustrates ancient astronomical cosmological ideas and seems to do justice to
the latest concepts of the presumed form of the universe. According to §33.3,
we can reduce the polar coordinates of the “P” to the simple scheme of Fig.
476.

Figure 476

Here the Origo 1/1 stands in the middle as the circle of unity;
from it, all < 1 ratios go inwards and all > 1 ratios go outwards. Every
ratio (= being-value) has its own sphere (circle) and its angle (= direction =
vector) within the circle periphery, which we identify with the octave. Thus we
have a domain of contraction, gravity, concentration, attraction (within the 1/1 circle), and a domain of unfolding,
evaporation, expansion (outside the 1/1 circle). These domains obey the symbols:

0 ← 1/1 → ∞

We will soon see that with this harmonic prototype, we come very close to
the real story of the emergence of the planetary bodies and their gravitational
relationships. I demonstrated in my “Tonspektren” (Abhandlungen) that various
atomic laws and primal ideas can be derived from it, and the fact that
it corresponds precisely to the image of the Pythagorean cosmos will be briefly
intimated near the end of this chapter.

Regarding
this polar representation of the “P”, it is interesting that here the 0/0
(Eidos) disappears along with its “envoys,” the equal-tone lines. This is a
pointer for the fact that the harmonic polar coordinates are more signatures
for aspects of the cosmos realizing itself in forms, while the familiar “P” not
only gives us information about material elements and backgrounds, but also
about the spiritual ones.

As
a conclusion to the didactic part of our textbook, we turn once again to our
venerable experimental instrument, the monochord. It will give us information
about a theorem which, although very insignificant in itself, opens up problems
of very far-reaching perspectives, and is of exceptional interest in various
regards.

Namely,
the theorem of the “metaphysical remainder.”

The Metaphysical Remainder

By “remainder,” we mean that part of the string that remains
left over, in all monochord experiments, from a fixed bridge point x/y
to the 0/00/10/2 ... 0/∞ line. In general
it does not matter whether, with the bridge point at 2/5e¢ (for 1/1 = c),
I pluck and sound the segment 2/5e¢ or the segment 3/5a. In the first case the remainder is 3/5, in
the second it is 2/5. But in a particular case we will
have to hold to one or the other
arrangement.

Now when we “realize” the
“P” system in its wavelengths (string-length ratios) using the monochord, we
can only ever set the monochord up so that the string is bounded on one side by
the 0/00/10/2 line, on the other side by the 0/01/12/2 ... line. If we now
draw the equal-tone lines, through which every ratio on the monochord realizes
its tone-number and tone-value, then we will observe that above, at the “head”
of the monochord, i.e. where it touches the 0/00/10/2
line, there is always an empty space left over, a remainder, regardless of how
large the index is set. For when I draw the equal-tone lines out from the 0/0 through all ratios of the uppermost row 1/11/21/3
..., this remainder remains always the same, and is never exceeded, with
constant size of the field 0/00/11/11/0. With this type of illustration (see
Fig. 477) one can also speak of a “constant.” This remainder, tangent to the
“metaphysical” domain of the 0/0 series and surrounded by
the two transcendent vectors 0/∞ and ∞/0,
is only relative in its “size,” as images 1-6 in Fig. 477 immediately show. The
relationship to the string unity diminishes rapidly as the index increases,
proportionally to the index in question. If I fix the unit instead of the
remainder, as Fig. 478 shows, then this remainder, i.e. the fundamental length
of the monochord 1/1, always remains of the same size, but the “metaphysical remainder” quickly
becomes smaller with an increasing index. Here one can no longer speak of a “constant”
remainder, but only of an ever-diminishing one. In both cases, the result is that
this remainder diminishes more and more with increasing indexes in relation to
the monochord unit, up to index ∞ where it ...?

The mathematician would
say here: “... disappears.” And it is evident that at index ∞ the
remainder becomes so minimal, falls so far short of every “size,” that we can
“neglect” it both practically and ideally. On the other hand, there is the
indubitable fact, visible in Figures 477 and 478, that this remainder must and
will endure in some size identical to 0/0 → 1/1, even at index ∞, and that for this
reason, we cannot eliminate it.

Figure 477

Figure 478

Every mathematician will
immediately know that this is related to the ancient problem or controversy of
the “differential quotients,” and that this dilemma retains the same antinomic poignancy
in the axiomatics of modern infinitesimal calculus as it did at the time of its
discovery by Newton
and Leibniz.

The harmonic approach to
it should then interest us all the more.

In the harmonic way of
thinking, the monochord represents the realization of the being-values in time
(frequency), space (wavelength), and number (causality). This “realization”
naturally resides in the diagram itself, and thus far the monochord is more the
visual display of the “P”, and above all the practical possibility of direct
sensory realization through the ear. This monochord is limited on the one side
by the unit, and on the other side it touches a line whose vector we designate
with the symbol 0/∞ (not arbitrarily, but
legitimately yielded from the “P” system!) and which we designated above as “Nothing
= absolute limit, maximal concentration” etc., in short with a purely abstract,
metaphysical expression. But only the monochord pushes forward up to this
metaphysical limit 0/∞; the equal-tone lines of the
individual being-values reach only up to the line of the “relative nothing” 1/∞ (n/∞), and it is
precisely this “metaphysical remainder” between the vectors n/∞
and 1/∞ (n/∞) that obtain a new, or a first,
interpretation through harmonics. This is no longer about a negligible or
non-negligible “quantity” dx, but
instead this infinitely small but enormously important step from the relative
into the absolute “Nothing” of the entire cosmological configuration. To this
is added, on the other side of the system, the polar correspondence of the two
vectors ∞/0 (= infinite, absolute expansion) and ∞/1 (∞/n) (= relatively
infinite, concrete infinity concepts), which our monochord does not touch, but
which sets the entire “P” system at index ∞ in this enormous tension,
precisely due to its polar correspondence to 0/∞
and 1/∞, which we believed we could propose as the origin for a future
world-renewing process. The very visual and symbolically instructive
illustration of Figures 477 and 478 shows the deeper background of this
tension, which we may safely call “epistemological.” The greater the indexes of
the “P” become, the more the unit of the monochord “fills out” with ratios,
i.e. the more restlessly the system of matter operates, the smaller the “metaphysical
remainder” becomes—in this case the metaphysical “substance”—until it is
finally “pressed to the wall” so much that in terms of matter, it becomes
almost nothing!

For a deeper meditative
observation, however, it is precisely this “metaphysical remainder,” i.e. what
still remains of a metaphysical “remnant,” albeit minimal, that is the key to
the solution of the whole cosmological puzzle, and if we observe its purely
mathematical formulation in the symbol dx,
then we can say without going too far that the differential quotient contains a
metaphysical problem of the first and foremost order, and that its harmonic
“formulation” gives it a deepening and amplitude, which the mathematical symbol,
together with its merely logical concept construction, does not attain.

History

On “self-awareness” and
“regeneration.”

The self-potentiation of
every being-value by 0/2, i.e. by the doubled Nothing
that is simultaneously everything, changes it into the Origo 1/1 and can be understood in its most extreme
sense as the monastic, ascetic way, but in general as tending toward the
concentration of the highest creative-value of every being-realization. In
contrast—here we anticipate—the recollection of the being-value by means of its
“equal-tone line” to the Eidos 0/0 no longer actually signifies a self-awareness,
but an identification of the “self” with the deity. Here monasticism and
asceticism lose their meaning, due to which all mystics who take this “direct”
path regard the substantiality of their Being, the “potentiation” of their
being-value in the personal God-concept of the Origo 1/1 and thus all monastic and ascetic isolation,
as secondary if not absolutely nothing, and direct their entire inner thought
and aspiration toward the “vision” of the Eidos 0/0.

That which we named
“regeneration,” the liquidation of collective conditions that have become unstoppable
and caught in insoluble tangles, and the going back (which admittedly is often
viewed as “going forward” in the sense of some kind of modernism!) to newly
visible, simpler situations, has always been connected with the concept and the
fact of “revolution,” a “renewing,” reformation (renaissance, rebirth), which,
as the last words express, not only represents a reversal of the existing, but
also a return to simpler norms, inherent a
priori in humanity. Now whether we observe this regeneration
harmonically as a reemphasis of normative selective elements or as a
renaissance of simpler cycles, it will always be connected with a rectification
of the “correct,” the “in tune,” in short, of the harmonic, and an abolition or
at least an attempted disarming of the dissonant. Should such a revolution be
contrived, however, by purely negative powers and sink into evil, it leads either
to the catastrophe of entire cultures or to a gigantic struggle between positive
and negative principles. Then at the end of the struggle, if the good wins, a
new cultural epoch begins.

This
struggle, which the individual must continually endure with himself and humans
amongst themselves, since life is not in a simple condition of equilibrium like
inorganic nature, but instead in an inner polar tension in the direction of the
divine, is, as we saw, represented prototypically in various ways in the “P”
system. As for the “war of the gods,” as so wonderfully symbolized by the inner
content of the fifth-diagram (§54.7), the various mythologies and religions
have always known of it.

“Ancient times they were

There Ymir dwelled

There was no sand nor sea

Nor salt waves

No earth below

Nor heavens above

Bottomless gaping

But nowhere grass.”

Thus
reads the third stanza of the famous ancient Germanic poem of world creation, Der Seherin Gedicht (Edda II in Thule, tr. by F. Genzmer, vol. II, 1920,
p. 35). Hardly was this great giant Ymir slain by the divine race of the Asen,
led by Odin, than the latter fell into a struggle with the second race of gods,
the Wanen. Stanza 13 of the above poem reads:

Only with difficulty can Marduk,
the god of light, put a stop to the gruesome deeds of Tiamat, catch her in a
“net,” and then destroy her:

“After he struck Tiamat,

Broke her forces, the hordes,

the gods, who went to her side to
help,

bowed trembling, turning back.

They sought to flee to save their
lives:

They were captured and flight was
impossible:

then he bound them all, destroyed
their weapons,

They sat in the snare, trapped in
the net.

The spheres resounded, filled with moaning ...”

In
Persian tradition (Schahrastani tr.
Haarbrücker I, 278, from Eisler, ibid., pp. 529-530) it reads: “A few
Zervanists believe that ... Ahriman ... found himself in a place separated from
heaven, but hatched his plots so long that he tore apart the heavens and
climbed upon them. Others say that he is in heaven and the earth is free from
him, but he hatched his plots so long that he tore apart the heavens and with
all of his beings climbed down to earth. The light with his angels fled, Satan
pursued him until he shut him in his garden [= paradise] and fought with him for
3000 years.” Further on it reads: “God created this world as a net for Ahriman, into which he has
fallen and in which he is held.”

The
image-concept of the “net” (already appearing in the Babylonian Epos)—to which
Eisler also dedicates almost all the content of his work Weltenmantel uns Himmelszelt (Munich, 1910), supporting it with
countless examples—is especially important conceptually in analogy to, and as a
background for, our prototypical idea of the tone-mesh of the “P”; but we must
forgo examples and refer the reader to Eisler’s work.

Also
in classical Greek mythology, much closer to us in its “human-like” figures,
there is a great battle of the gods at the very beginning, concentrated in the
archetypes of Gaea, Uranus, and Chronos. Chaos, incited through Eros (Love),
generates the dark heavy depths of Tartarus. From this originates Gaea, the
Earth, and Uranus, the Heavens (female and male principle), which generate the
Titans as the primal substance of formed life. But these Titans, including
Chronos, moaning muffled from the depths, shake the heart of their mother Gaea,
who then incites the youngest of her children, Chronos, against his own father Uranus.
Chronos castrates Uranus, the terrible deed disturbs the peace, rips evil and
good away from one another, and war follows. Uranus’s member, thrown in the
sea, gives rise to the “foam-born Venus,” the symbol of earthly love. True,
this somewhat alleviates the terrible tragedy, but still it allows full play to
the thoughts and original feeling of a dissension reaching into the deepest foundations
of the world and of consciousness.

When
we called the generator-tone line 0/01/12/23/3 ... ∞/∞ the “mediator line,” it was not only because
of its outer position in the diagram, but above all because of its inner
relationship to all ratios in the diagram. If we grasp this line prototypically
as a unity of the creative force, forever passing through the entire spatial-temporal
cosmos, always present and ever repeating, then it symbolizes a principle
common to all religions and most mythologies: the redeemer principle, or the mediator
principle, i.e. a force that releases the being-value from its spatial-temporal
entanglement, and through assimilation to unity leads it back into the deity.
The 1/1
emanating from the Eidos 0/0, the concept of a personal God, requires an
enduring, ever-repeating self-realization, a “proxy” in the domain of
historical reality. Only the Origo as a continuously repeating existential fact
holds the “P” system in psychophysical equilibrium, and right from the basis, our
religious conduct is required to manifest this prototype, unconsciously present
in us from the beginning, again and again in image-concepts and religious
psychical forms.

Instead of giving examples
of this idea of a savior and its various manifestations, I refer to the
excellent work of Alfred Jeremias: Die
außerbiblische Erlösererwartung (Berlin,
1927), in which the reader is presented with comprehensive material, discussed with
thorough responsibility and strong spiritualization. In the introduction to his
work, Jeremias writes: “The most important theorems which this book will prove,
on the basis of the sources and their spiritual-historic interpretation, are
these: Human culture is a unified whole, and at its core is religion. Human
religion is a unified whole, and at its core is the expectation of a savior.
The individual religions of the world are to each other as sects are to one
religion, or as dialects of a spiritual language. And the original Christianity
is the fulfillment of religion.”

Our above mentioned view (based
on the limes∞/∞ of the Origo line) of a limit of the universe
reached with this limes, and thus a
necessary world-collapse, is likewise a most ancient idea of the religions,
mythologies, and wisdom. In the above mentioned ancient Germanic poem of the
creation of the world, stanza 44 reads:

“The sun goes out

The land sinks into the sea

From heaven fall

The holy stars.

Smoke and fire

Roar below

High heat

Climbs skywards.”

One need only speak the
word “apocalypse” to know and understand that this important harmonic prototype
also tended toward corresponding ektypic image-concepts among early people who
were as yet unspoiled, and still possessed an inner magical vision.

“The
destruction and recreation happens according to Indian wisdom through the world-burning. The seeds of all things
are thrown into the womb of Bhavani, whose image is the lotus, and thus a new
world can exist once again. This dogma of world-fire (̕εκπύρωσις) is
specifically designated as Orphic by many authorities. Refer merely to Plutarch
(De defectu oraculorum), Proclus (on
Plato’s Timaeus II, p. 99), Clement
of Alexandria (Stromata, V). Commonly this doctrine is
also called Heraclitean, and there can be no doubt that in the system of
Heraclitus it was very highly developed; which, incidentally, also speaks for
the relatively early knowledge of it on the part of the Greeks. An agreement
with the Indian type of idea appears immediately in the Heraclitean fragments,
in the approach of the fire-wind [the Blitz!](πρηστήρ) that sets the world
on fire. The world-fire was also a main theme in the Stoic system. According to
this, after the universal destruction, Zeus alone remains, who takes everything
into himself and preserves it. If the Orphic schools followed oriental sources,
as they doubtless did, they presumably taught, like their sources, of the
persistence of the world-substance during the burning of the individual things.
This is also suggested by the teachings of Proclus (in Timaeus ibid.) on the re-gathering of things into God as an
Orphic doctrine.”

Finally, we shall give one
more historical example for an application of the polar “P” (“P” as polar
coordinates). Fragment 7 of Philolaus (Diels: Fragmente der Vorsokratiker, 3rd ed., vol. I, 1912, p.
312) proclaims: “The first composite, the One at the center of the Sphere, is
called the Hearth.” Fragment 17 (ibid. pp. 316-317) proclaims: “The universe is
one, and it began to come into being from the center, and from the center
upwards at the same intervals as those below. For the parts above from the
center are in inverse relationship to those below; for the center is to what is
below as it is to what is above, and so with all the rest; for both stand in
the same relationship to the center, except insofar as their positions are
reversed.”

The reader, at this point,
should once more observe Fig. 476, or any of our polar depictions of the “P”.
Here the Philolaic or Pythagorean cosmos is revealed in a completely
unconstrained manner, whereby one should consider that this kind of tone-number
illustration or conversion was certainly known to Philolaus, an outspoken
Pythagorean. “The One at the center of the Sphere = hearth” is the circle of
the unity 1/1. If the world order appeared “from the center, in the same intervals
upwards as downwards,” and “what lies above the center [outside the 1/1 circle] is in inverse relationship to what is below
[within the 1/1 circle]”—then this is also a precise description of Fig. 476; because the
octaves (as framework for the sequence of ratios) go out from the 1/1 circle in opposite directions. And when it
finally reads: “for both directions are the same in their relationship to the
center [i.e. the 0-point], except they are reversed,” this is once again a
precise description of the “equal” line (vector) of the c-tone with its octaves; they simply turn around on the periphery
of the 1/1
circle, i.e. one is directed outwards, the other inwards. In all the literature
on Pythagoras, I have found not even a slightly satisfactory solution for this
theorem. I offer it here yet again, even though I have already published it in
my “Pythagorasaufsatz” (Abhandlungen
1938) with many other interpretations of Pythagorean fragments regarding which
philology has hitherto been more or less helpless.

A. von Thimus, in his Harmonikale Symbolik (vol. I, pp. 265
and 339 ff.), mentions the Celtic bards (“those Pythagoreans of the North”) and
Druidism, which finally died out in the old Irish and English
monastery-schools, although its peculiarities still endured well into the
Middle Ages. He quotes, from Ferdinand Walters’ Das alte Wales (Bonn, 1859), a few remarkable statements from the
“Trioedd Barddas” (Theological Triads), of which one is repeated here, since
its conceptual image has an astonishing similarity to the above Pythagorean
idea: “There are three circles (or conditions) of being: the circle of infinity,
where nothing exists, living or dead, except for God, and only God can traverse
it; the circle of the beginning, where all natural things rise up out of death,
and which humans must traverse; and the circle of happiness, where all things
spring from life; humans will traverse this circle in heaven.” If we use the
concept of “condition” here instead of “circle,” then we can equate the first
circle to the outermost condition n/1, the second with
the condition 1/1, and the third (the center, where humans and all other things emanate,
i.e. become conscious of themselves in highest concentration) with the
condition 1/n.

§54.8. Results of Harmonic
Cosmogony

According to akróasis, the
world emerged from a depth (Eidos 0/0) that cannot be explored, and can only be
insufficiently described with words, by virtue of an act of self-examination
and self-beholding. Harmonics thus proposes an act of creation at the
“Beginning” of the world, but not a creation from the Nothing (0), but instead
a creation from the All (0/0). The sinking back or rising up into the All (0/0) that is necessary with the end of the world (∞/∞) thus means not absolute annihilation, but
instead the possibility of a total renewal. In the act of creation (Origo 1/1), the first being-value is realized. The
“being” is in reciprocity of frequency and wavelength, with which time, space,
and causality (number), as well as inversion to itself, is born. The “value” sounds and
produces the word, the Logos. The temporal element of the being-value
(frequency) symbolizes the will; it evolves a long series of forms (history),
at the end of which is love. The spatial element of the being-value
(wavelength) simply symbolizes the (material) “gestalt”; it evolves a long
series of spatial forms, at whose end stands the order of the cosmos and whose
concentration is the human form. The tonal element of the being-value (tone,
sound) symbolizes the “word” in general; it evolves a long series of forms, at the
end of which is the psychical and spiritual expression of man. Harmonics
summarizes the synthesis of all these elements in the concept of “akróasis.” In
the first evolution of the unity (Origo), the Trinity is born, and with it the
interval of the octave (the octave of Pythagoras), the framework-interval,
within which the entire subsequent development at last becomes possible and
obtains its stepwise significance. In principle, with this creation-triad the
creation polarity is also given, which is already based in nuce on the inversion in the Origo. The concepts and conditions of
the Nothing (0) and the Unending (∞) emerge, as well as the unending
plethora of being ∞/∞, first as directions, vectors—then limited in
the relevant symbols themselves. The world shows itself spread within this
polarity in the three principles of the limiting (1/∞) (atom, darkness, inhaling, female, passive,
attraction, etc.), the unlimited (∞/1) (universe, light, exhalation, male, active,
repulsion, etc.), and the equal (n/n, ∞/∞) (equilibrium, balance, mediating principle).
Within these principles, all the development of nature unfolds. The first
“senary” cycle, the appearance of the “foreign” seven-series, the analysis of
the fifth-diagram, etc., show that there are disturbance factors inherent a priori in the harmonic cosmology,
which can only be overcome, or built in, rebuilt, through human “retrospection,”
be it upon the Eidos, the Origo (middle line), or upon simpler selective norms.
Only within these selections do we step outside the simple necessity of nature,
only here can we “express” ourselves and create a realm of human freedom in the
direction of the Beautiful and the Good.

This is the great
framework of harmonic cosmogony. All chapters of this book will be useful for
completing it in detail.

One might say that this
“result” offers little that is new, and has already been realized in its
characteristic features in some way in the religion, philosophy, and art of all
times and peoples—which indeed our ektypic examples prove. This is undoubtedly
correct. But beside the fact that there will hardly ever be a doctrine that is
able to unify in itself such a great number of heterogeneous things, and to
bring them into a sensible relationship with one another, harmonics is still
about something more than a simple intellectual synthesis. All harmonic forms
and entities are not only intelligible products of logical deliberations, but are
also anchored in nature and in our psyche,
and precisely this double foundation secures them a substantially persuasive
epistemological weight. In harmonics we are no longer directed only to belief, to factual knowledge, or
to logical conclusions, which often enough can be brought into contact with
each other with difficulty or not at all. By virtue of its approach to the
primal phenomenon of tone-number, akróasis takes its soundings a priori in nature and in our psyche, and this very fact
makes its results compelling in a completely different way. What is important
is not the simple connecting and systematizing from some ”holistic” or other
viewpoint—although this can and must be so under certain conditions—but the
leading back to a common root which we can physically and psychically control.
And this is precisely what our harmonic studies are about. I have emphasized
continually, in all my writings, the fact that this also represents only a
single “road to Rome,”
and have checked myself against a hypertrophy of harmonic ambitions. But finally,
it is important to “get to Rome” one way or another; the
fact that there may be more or less difficult ways there, straight ways and
roundabout ways, is secondary.

§54.9. Bibliography

For
2 and 3, see §25 of this book. For 4, see §30. For 5, see §23. For 6, see §26.
For 7, see §13-§16, and §24 (equal-tone lines). Furthermore: H. Kayser: Akróasis, last section.